Finite Group Databasebeta

← #15672487

Subgroups — #15672487

Order 2944.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093070C211yesmaximal, characteristic, complemented
2#13092765C211yesmaximal, characteristic, complemented
3#13092613C211yesmaximal, characteristic, complemented
4#13092613C211yesmaximal, characteristic, complemented
5#13092144C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#332C211yesmaximal, characteristic, complemented
8C2×#67292—21no—
9C23×C4⋊Q8C2211yescharacteristic
10#10625117—21no—
11C2×D184—21no—
12C2×D184—21no—
13#10625066—21no—
14#10625065—22no—
15C4⋊C4×D23—21no—
16#10625045C2211yescharacteristic
17C4×D92C2211yescharacteristic
18C4×D92C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic
21#10625003—21no—
22#10625003—21no—
23#10624991—22no—
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26#67292—42no—
27#67292—42no—
28C2×D92—22no—
29C2×D92—21no—
30C2×D92—21no—
31C2×D92—21no—
32C2×D92D411yescharacteristic
33C2×D92D411yescharacteristic
34C2×C4×D23—22no—
35C2×C4×D23—21no—
36C2×C4×D23—21no—
37C2×C8×C23—21no—
38C2×C8×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D412yes—
41C42×C23C2311yescharacteristic
42(C2×D23)⋊C4—22no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23D411yescharacteristic
46C4⋊Dic23D411yescharacteristic
47Dic23⋊C4—22no—
48C2×C23⋊C8—21no—
49D184—42no—
50D184—42no—
51C22×D23—21no—
52C22×D23—21no—
53C22×D23—41no—
54Q8×C23—41no—
55Q8×C23—41no—
56C2×C4×C23—22no—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C2×Dic23—21no—
61C2×Dic23—21no—
62D92—21no—
63D92—21no—
64D92—21no—
65D92—42no—
66D92—44no—
67D92—41no—
68D92—41no—
69D92—41no—
70D92—41no—
71D92D812yescomplemented
72C4×D23—44no—
73C4×D23—41no—
74C4×D23—41no—
75C4×D23—41no—
76C4×D23—41no—
77C8×C23—41no—
78C8×C23—41no—
79C23⋊C8—41no—
80#1625—231nomaximal, Sylow
81C22×C23#12011yescharacteristic
82C2×D23—22no—
83C2×D23—41no—
84C2×D23—41no—
85C2×D23—41no—
86C2×D23—41no—
87C2×D23—41no—
88C2×D23—81no—
89C2×D23—81no—
90C2×D23—81no—
91C4×C23—21no—
92C4×C23—42no—
93C4×C23C2×D811yescharacteristic
94C4×C23#13511yescharacteristic
95C4×C23AGL(1,ℤ/8)11yescharacteristic
96C4×C23AGL(1,ℤ/8)11yescharacteristic
97Dic23—41no—
98Dic23—41no—
99#547—231no—
100#486—231no—
101#459—231no—
102#459—231no—
103#332D2311yescharacteristic, complemented
104D4⋊C8—231no—
105D4⋊C8—231no—
106C2×C23#44711yescharacteristic
107C2×C23#44911yescharacteristic
108C2×C23#45411yescharacteristic
109D23—42no—
110D23—81no—
111D23—161no—
112C2×#41—461no—
113C2×D8—461no—
114C2×D8—461no—
115C4⋊Q8C2×D2311yescharacteristic
116#127—231no—
117#123—462no—
118C22⋊Q8—461no—
119#121—461no—
120C4×D4—231no—
121C4×D4—231no—
122C2×C4⋊C4—461no—
123C4⋊C8C2×D2311yescharacteristic
124C4⋊C8C2×D2311yescharacteristic
125#102—461no—
126#102—461no—
127#102—462no—
128C4×C8—231no—
129C23#162511yescharacteristic, complemented, Sylow
130#41—922no—
131#41—922no—
132C2×Q8—21no—
133C2×D4—231no—
134C2×D4—231no—
135C2×D4—462no—
136C2×D4—461no—
137C2×D4—461no—
138C2×D4—461no—
139C22×C4—462no—
140C22×C4—461no—
141C22×C4—461no—
142D8—922no—
143D8—922no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—461no—
147C4⋊C4—21no—
148C4⋊C4—231no—
149C4⋊C4—231no—
150C4⋊C4—462no—
151C4⋊C4D9212yes—
152C22⋊C4—462no—
153C22⋊C4—461no—
154C22⋊C4—461no—
155C42C22×D2311yescharacteristic
156C23—461no—
157C23—461no—
158C23—921no—
159Q8—41no—
160Q8—41no—
161D4—232no—
162D4—461no—
163D4—461no—
164D4—461no—
165D4—922no—
166D4—924no—
167D4—921no—
168D4—921no—
169D4—921no—
170D4—921no—
171C2×C4—22no—
172C2×C4—461no—
173C2×C4—461no—
174C2×C4—924no—
175C2×C4—921no—
176C2×C4—921no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4C2×D9211yescharacteristic
180C2×C4D4×D2311yescharacteristic
181C2×C4D4×D2311yescharacteristic
182C8—41no—
183C8—41no—
184C8—921no—
185C22—462no—
186C22—921no—
187C22—921no—
188C22—921no—
189C22—921no—
190C22—921no—
191C22—1841no—
192C22—1841no—
193C22—1841no—
194C22#1062505311yescharacteristic
195C4—21no—
196C4—42no—
197C4—921no—
198C4—921no—
199C4D8×D2311yescharacteristic
200C4#1062508511yescharacteristic
201C4#1062508511yescharacteristic
202C4#1062509011yescharacteristic
203C2—922no—
204C2—3681no—
205C2—1841no—
206C2#1309255211yescharacteristic
207C2#1309256511yescharacteristic
208C2#1309259211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#332C2
socleC22×C23#120
hypercenter#332D23
hypocenterC23#1625
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13093070C2semidirect
2. #13092765C2semidirect
3. #13092613C2semidirect
4. #13092613C2semidirect
5. #13092144C2semidirect
6. #13092144C2semidirect
7. C23×#332C2semidirect
71. D92D8semidirect
103. #332D23semidirect
129. C23#1625semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130930702
#130927652
#130926132
#130921442
C23×#3322
#162523